Probing three-state Potts nematic fluctuations by ultrasound attenuation

TL;DR

This paper investigates how three-state Potts nematic fluctuations influence phonon properties in materials like twisted bilayer graphene, proposing ultrasound attenuation as a key experimental signature of these fluctuations and their critical behavior.

Contribution

It introduces a method to identify three-state Potts nematic fluctuations via ultrasound attenuation and analyzes their isotropic effects on phonons and phase transition characteristics.

Findings

Ultrasound attenuation shows isotropic divergence near nematic criticality.

Nematic phase transition is weak first-order near van-Hove singularity.

Impurity effects can shift the transition from first-order to second-order.

Abstract

Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer graphene and doped-Bi$_2$Se$_3$, we analyze the impact of critical nematic fluctuations on the low energy properties of phonons. In this study we propose how to identify the three-state Potts nematic fluctuations by ultrasound attenuation. The Gaussian fluctuation analysis shows that the Landau damping term becomes isotropic due to fluctuations of the $C_{3}$-breaking bond-order, and the nemato-elastic coupling is also shown to be isotropic. These two features lead to an isotropic divergence of the transverse sound attenuation coefficient and an isotropic lattice softening, in contrast to the case of the $C_4$-breaking bond-order which shows the strong anisotropy. Moreover, we use a mean-field approximation and discuss the impurity effects. The transition temperature takes its maximum near the filling of the van-Hove singularity, and the large density of states favors the nematic phase transition. It turns out that the phase transition is of weak first-order in the wide range of filling and, with increasing the impurity scattering, the first order transition line at low temperatures gradually shifts towards the second-order line, rendering the transition a weak first-order in a wider range of parameters. Furthermore, it is confirmed that the enhancement of the ultrasound attenuation coefficient will be clearly observed in experiments in the case of a weak first-order phase transition.